Internal problem ID [12208]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 158.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y=2 x +3} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+5*diff(y(x),x)-2*y(x)=2*x+3,y(x), singsol=all)
\[ y \left (x \right ) = -x -4+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{x} x \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 31
DSolve[y'''[x]-4*y''[x]+5*y'[x]-2*y[x]==2*x+3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^x+x \left (-1+c_2 e^x\right )+c_3 e^{2 x}-4 \]